Abstract
This paper examines the linear complexity of a family of generalized cyclotomic binary sequences of period \(p^n\) recently proposed by Xiao et al. (Des Codes Cryptogr, 2017, https://doi.org/10.1007/s10623-017-0408-7), where a conjecture about the linear complexity in the special case that \(f=2^r\) for a positive integer r was made. We prove the conjecture and also extend the result to more general even integers f.
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Acknowledgements
The authors are very grateful to the anonymous reviewers and the Editor for their comments that improved the presentation of this paper. V. Edemskiy was supported by the Russian Ministry of Education, project No. 8.7367.2017/8.9. C. Li and T. Helleseth were supported by the Research Council of Norway under Grant 247742/O70. C. Li was also partly supported by the research project (No. 720025) from UH-nett Vest in Norway. X. Zeng was supported by National Natural Science Foundation of China under Grant 61472120 and National Natural Science Foundation of Hubei Province of China under Grant 2017CFB143.
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Edemskiy, V., Li, C., Zeng, X. et al. The linear complexity of generalized cyclotomic binary sequences of period \(p^n\). Des. Codes Cryptogr. 87, 1183–1197 (2019). https://doi.org/10.1007/s10623-018-0513-2
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DOI: https://doi.org/10.1007/s10623-018-0513-2